Sunday, August 10, 2014

KAVR into Farad; Capacitor KVAR conversion into Farad

Below we study how to
Convert Farads into kVAR and Vice Versa. It usually comes in the mind that capacitor used for motors or higher capacity inductive load is in KVAR but capacitor rating is in farad . Then how we can convert KVAR into Farad.

A Single phase 400V, 50Hz,
motor takes a supply current of 50A at a P.F (Power factor) of 0.6. The motor
power factor has to be improved to 0.9 by connecting a capacitor in parallel
with it. Calculate the required capacity of Capacitor in both kVAR and Farads.

Solution.:

(1) To find the required
capacity of Capacitance in kVAR to improve P.F from 0.6 to 0.9 (Two Methods)

Solution #1 (By Simple Table
Method)

Motor Input = P = V x I x
Cosθ

= 400V x 50A x
0.6

= 12kW

From Table, Multiplier to
improve PF from 0.60 to 0.90 is 0.849

Required Capacitor kVAR to
improve P.F from 0.60 to 0.90

Required Capacitor kVAR = kW
x Table Multiplier of 0.60 and 0.90

= 12kW x 0.849

= 10.188 kVAR

Solution # 2 (Classical Calculation
Method)

Motor Input = P = V x I x
Cosθ

= 400V x 50A x
0.6

= 12kW

Actual P.F = Cosθ1 = 0..6

Required P.F = Cosθ2 = 0.90

θ1 = Cos-1 = (0.60) =
53°.13; Tan θ1 = Tan (53°.13) = 1.3333

θ2 = Cos-1 = (0.90) =
25°.84; Tan θ2 = Tan (25°.50) = 0.4843

Required Capacitor kVAR to
improve P.F from 0.60 to 0.90

Required Capacitor kVAR = P
(Tan θ1 - Tan θ2)

= 5kW (1.3333– 0.4843)

= 10.188 kVAR

(2) To find the required
capacity of Capacitance in Farads to improve P.F from 0.6 to 0.9 (Two Methods)

Solution #1 (Using a Simple
Formula)

We have already calculated
the required Capacity of Capacitor in kVAR, so we can easily convert it into
Farads by using this simple formula

Required Capacity of
Capacitor in Farads/Microfarads

C = kVAR / (2 π f V2) in
microfarad

Putting the Values in the
above formula

= (10.188kVAR) / (2 x π x 50 x 4002)

= 2.0268 x 10-4

= 202.7 x 10-6

= 202.7μF

Solution # 2 (Simple
Calculation Method)

kVAR = 10.188 … (i)

We know that;

IC = V/ XC

Whereas XC = 1 / 2 π F C

IC = V / (1 / 2 π F C)

IC = V 2 F C

= (400) x 2π x (50) x C

IC = 125663.7 x C

And,

kVAR = (V x IC) / 1000 …
[kVAR =( V x I)/ 1000 ]

= 400 x 125663.7 x C

IC = 50265.48 x C … (ii)

Equating Equation (i) &
(ii), we get,

50265.48 x C = 10.188C

C = 10.188 / 50265.48

C = 2.0268 x 10-4

C = 202.7 x 10-6

C = 202.7μF

Good to Know:

These are the main Formulas
to Convert Farads into kVAR and Vice Versa